Question

The length of a simple pendulum executing simple harmonic motion is increased by $21\%$. The percentage increase in the time period of the pendulum of increased length is

• A. $11\%$
• B. $21\%$
• C. $42\%$
• D. $10\%$

Answer 1

Answer: (D)

Time period of simple pendulum is given by.
$T=2\pi \sqrt{\frac{\ell }{d}}$
New length ${\ell }^{\prime }=\ell +\frac{21}{100}\ell =\frac{21}{199}\ell$
$\therefore \frac{T^{\prime }}{T}=\sqrt{\frac{{\ell }^{\prime }}{\ell }}=\sqrt{\frac{21}{100}}$
$\frac{T^{\prime }}{T}=\frac{11}{10}$
$\Rightarrow T^{\prime }=T+\frac{1}{10}T$
$T\ne 10\%$ of $T.$